[See] Let X_1, X_2, ..., X_n be a random sample from a two-parameter (shifted) exponential distribution with the following p.d.f. f(x)=
Question: Let \(X_{1}, X_{2}, \ldots, X_{n}\) be a random sample from a two-parameter (shifted) exponential distribution with the following p.d.f.
\[f(x)=\left\{ \begin{array}{*{35}{l}} \frac{1}{\theta }{{e}^{-(x-\delta )/\theta }}, & \text{ if }\delta x\infty ; \\ 0, & \text{ otherwise } \\ \end{array} \right.\]- Find the mean and variance of this distribution.
- Find the method of moments estimators \(\tilde{\delta}\) and \(\tilde{\theta}\) of \(\delta\) and \(\theta\), respectively.
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Use the following data to give point estimates of \(\delta\) and \(\theta\).
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